We present an approach to uncertainty quantification for nuclear applications that combines the covariance evaluation of differential cross-section data and the error propagation from matching a criticality experiment using a neutron-transport calculation. We have studied the reduction in uncertainty of 239Pu fission cross sections by using a one-dimensional neutron-transport calculation with the PARTISN code. The evaluation of 239Pu differential cross-section data is combined with a criticality measurement (Jezebel) using a Bayesian method. To quantify the uncertainty in such calculations, we generate a set of random samples of the cross sections, which represents the covariance matrix, and estimate the distribution of calculated quantities, such as criticality. We show that inclusion of the Jezebel data reduces uncertainties in estimating neutron multiplicity.